Something I randomly thought about

Hello, I'm interested in finding a general way to solve equations like the one below;

 

x+y+z=17, 

xy+xz+yz=94,

xyz=168

 

something along the lines of:

x+y+z=a

xy+xz+yz=b

xyz=c

 

Where all variables are real.

I know this is linked to the cubic formula through vietas equations for cubics, but I was wondering if there's a way to find these without a link to cubics.

 

Thanks for any leads.